South Korea’s cancellation of a key intelligence-sharing pact with Japan has triggered a growing diplomatic spat with Washington that analysts say weakens President Trump’s North Korea policy and throws into question the three-way alliance underpinning American security architecture across Asia.

With South Korea summoning U.S. Ambassador Harry Harris last week to demand that Washington tone down its criticism, the Trump administration is facing calls to tread with care in its efforts to contain the rift between its two East Asian allies.

“The administration needs to do more to salvage this thing and not just criticize Seoul for dropping it,” said Patrick Cronin, the Asia-Pacific security chair at the Hudson Institute in Washington.

“We have the two alliances, but the whole point is that they are the basis on which we build a much larger regional security architecture that’s advancing our interests and values across the region,” Mr. Cronin told The Washington Times. “If our two key pillars are wobbly … we don’t look like we are an effective leader.”

Others warn that the feud puts in jeopardy Mr. Trump’s signature diplomatic overture: the pursuit of nuclear diplomacy with North Korea. U.S. efforts to woo Pyongyang have relied heavily on lockstep coordination with the government of South Korean President Moon Jae-in over the past two years.

David Maxwell, a former U.S. Special Forces officer and senior North Korea analyst at the Foundation for Defense of Democracies, said the “cracks in the armor of the alliance” between the U.S. and South Korea — commonly referred to as the Republic of Korea, or ROK — will affect the North Korea policy and could worsen dramatically.

“There will be no successful outcome on the Korean Peninsula or in Northeast Asia unless there is a foundation of a strong ROK/U.S. alliance and Japanese/U.S. alliance and effective trilateral coordination, collaboration and cooperation,” Mr. Maxwell wrote in comments circulated to reporters Friday.

By some measures, the cracks in the armor have been widening for several years while Washington turned a blind eye on the assumption that Japan and South Korea would find a way to work together as fellow democracies aligned against the prospect of an increasingly influential and militarized communist China.

But the two nations have a tortured past that includes Japan’s colonial occupation of the Korean Peninsula from 1910 to 1945. South Koreans still bristle at Japan’s treatment of the country, first as a colony in the early 20th century and then during World War II.

The government of Japanese Prime Minister Shinzo Abe contends Tokyo has long since made reparations for its actions and has become outraged over what it sees as an attempt by the Moon administration in Seoul to revive historical grievances for domestic political gain.

The Japan-based Nikkei Asian Review has pointed to the specific issue of South Korean court rulings since Mr. Moon came to office that have ordered the Japanese companies Mitsubishi Heavy Industries and Nippon Steel & Sumitomo Metal to compensate the families of South Korean workers for unpaid labor during World War II.

Friction over the issue escalated late last year when Tokyo suddenly accused a South Korean navy destroyer of targeting a Japanese aircraft with fire-control radar. The incident triggered rising acrimony as well as frustration among South Koreans that the Trump administration appeared to have sided with the Abe government in the clash.

Tokyo moved again this summer by announcing trade sanctions over what it said were more historical compensation demands from Seoul, targeting in particular exports vital to South Korea’s world-class technology sector.

The Japanese trade curbs in turn have triggered an outburst of anti-Japan sentiment in South Korea, marked by street protests, cancellations of vacations to Japan and widespread boycotts of Japanese beer, clothes and other products.

The most provocative move was Seoul’s Aug. 22 announcement that it was abandoning the General Security of Military Information Agreement on sharing intelligence with Tokyo. Mr. Moon approved the move despite the certain outrage it would spark in Washington.

Mr. Cronin suggested that Mr. Moon’s move reflected a growing unhappiness in Seoul with the Trump administration as well, as the euphoria over the outreach to North Korea has given way to a diplomatic slog.

He noted Mr. Trump’s repeated demands that South Korea pay more for the roughly 30,000 U.S. troops stationed in the country. Mr. Trump has also denigrated long-standing U.S.-South Korean military drills and given Pyongyang a pass on tests of short-range missiles that cannot reach the U.S. but threaten South Korea directly.

State Department spokeswoman Morgan Ortagus tweeted last week that canceling the intelligence accord “will make defending [South] Korea more complicated and increase risk to U.S. forces.” U.S. security officials are reportedly skipping the South Korean Defense Ministry’s annual Seoul Defense Dialogue this week.

Defense Secretary Mark Esper last week took an evenhanded stance. He told reporters he was “very disappointed that both parties are engaged in this,” but he also suggested that the matter remained an internal spat that Tokyo and Seoul should resolve.

Gen. Joseph F. Dunford, chairman of the Joint Chiefs of Staff, appeared with Mr. Esper at the Pentagon and said the intelligence pact’s demise could be overcome from a tactical perspective even if South Korea and Japan remain at odds.

“We have other ways of sharing information,” he said. “Obviously, none as effective as a very strong bilateral information-sharing agreement between the two countries, but there are other mechanisms in place to allow us to deal with alliance crisis or contingency.”

Mr. Cronin suggested that South Korea’s defiance on the intelligence-sharing pact with Japan, which U.S. officials spent more than two decades trying to establish, could be reversed if Washington takes a more sensitive tack with Seoul.

“If that means de-escalating our demands on South Korea for them to share more of the burden for defense spending, then so be it …,” he said. “It’s not worth getting even a few more billion dollars out of our ally if you’re going to break the whole security architecture that’s advancing our interests and values across the region.”

Key administration officials including Randall Schriver, assistant secretary of defense for Indo-Pacific security affairs, and David Stilwell, assistant secretary of state for East Asian and Pacific Affairs, “are thinking hard about this,” Mr. Cronin said.

“But I also think everybody wants to please the boss, and the boss wants a big win that shows our allies are willing to pay,” Mr. Cronin said. “I say be more creative. I’m not letting the South Koreans off the hook. I’m just saying the U.S. should consider being more agile and flexible on this than what we’re doing right now.”

It remains to be seen what, if any, lengths the administration is willing to go to persuade South Korea to mend its dispute with Japan.

Mr. Schriver expressed discontent that the Moon government had not forewarned the U.S. of its plans. He said at a Center for Strategic and International Studies forum last week that Seoul has a “serious misapprehension” about the security challenges in northeast Asia, according to the Reuters news agency.

But there are also concerns that too much U.S. pressure could trigger anti-American sentiment in South Korea. The pollster Realmeter found last week that roughly 55% of South Koreans said they agreed with the Moon government’s decision to scrap the intelligence-sharing accord.

An editorial in Chosun Ilbo, a generally conservative newspaper in Seoul, argued that U.S. officials have “pretty much sided with Tokyo” on the issue, but it also chided the Moon government. Summoning the U.S. ambassador was “unprecedented” and a sign that the government “will also now incite anti-American sentiment” ahead of parliamentary elections next year.

The bottom line, the editorial said, is that “the U.S.-Korea alliance, which remains the sole foundation of [South Korea‘s] defense, is being shaken.”